论文标题
duoidal $ \ infty $ - 经营模块类别
Duoidal $\infty$-categories of operadic modules
论文作者
论文摘要
在本文中，我们研究了$ \ infty $ $ $ $ - 经营模块类别。令$ \ mathcal {o}^{\ otimes} $为一个小型连贯$ \ infty $ -operad，让$ \ Mathcal {p}^{\ otimes} $为$ \ infty $ -operad。如果$ \ Mathcal {p} \ otimes \ Mathcal {o} $ - 单型$ \ infty $ -Category $ \ Mathcal {C}^{\ otimes} $有足够的colimits供应mod} _a^{\ Mathcal {o}}（\ Mathcal {c}）$的$ \ Mathcal {O} $ - $ a $ a $ a $ a $ a $ a $ a $ \ mathcal {c}^{\ otimes} $的结构具有$（\ Mathcal {p p} $的结构任何$ \ Mathcal {p} \ otimes \ Mathcal {o} $ - algebra object $ a $的$ \ infty $ - 类别。
In this paper we study duoidal structures on $\infty$-categories of operadic modules. Let $\mathcal{O}^{\otimes}$ be a small coherent $\infty$-operad and let $\mathcal{P}^{\otimes}$ be an $\infty$-operad. If a $\mathcal{P}\otimes\mathcal{O}$-monoidal $\infty$-category $\mathcal{C}^{\otimes}$ has a sufficient supply of colimits, then we show that the $\infty$-category ${\rm Mod}_A^{\mathcal{O}}(\mathcal{C})$ of $\mathcal{O}$-$A$-modules in $\mathcal{C}^{\otimes}$ has a structure of $(\mathcal{P},\mathcal{O})$-duoidal $\infty$-category for any $\mathcal{P}\otimes\mathcal{O}$-algebra object $A$.
